Fractional‐Order Diffusive Hopfield Models: Existence and Stability of Weighted Pseudo‐ S ‐Asymptotically ω ‐Periodic Solutions
Farah Dridi, Hediene Jallouli, Chaouki Aouiti · Mathematical Methods in the Applied Sciences · 2025
ABSTRACT This paper investigates a class of fractional‐order Hopfield neural networks with diffusive effects. We first establish fundamental properties of weighted pseudo‐ ‐asymptotically ‐periodic functions. Within this framework, and using tools from fractional calculus, Mittag‐Leffler functions, Fourier analysis, and the theory of the Laplacian operator, we prove the existence and uniqueness of a weighted pseudo‐ ‐asymptotically ‐periodic solution for the proposed model. The proof is based on the Banach fixed‐point theorem. Furthermore, we analyze the Mittag‐Leffler stability of the system. A numerical example is provided to illustrate the theoretical results and demonstrate their practical applicability.